Rovibrational spectroscopy of molecules boasts extremely high precision, but its usefulness relies on the assignment of spectral features to corresponding quantum mechanical transitions. In the case of ortho-H-2-CO, a weakly bound complex abundant in the interstellar medium (although not yet observed there), the rather complex spectrum has been unexplained for more than a decade. We assigned this spectrum by comparison with a purely ab initio calculation. For most lines, agreement to within 0.01 centimeter(-1) between experiment and theory was achieved. Our results show that the applicability of rovibrational spectroscopy can be extended with the assistance of high-accuracy quantum mechanical computations.